This set of equations reduces to the standard active Brownian particle model [1]}, [2]} for the vanishingly small viscous relaxation time. In the above equations, \(\lbrace x, y\rbrace \)  is the instantaneous position of the particle's center of mass. It is assumed that self-propulsion force with a constant modulus \(F_0\)  (or \(v_0\) ) is directed along a certain particle's symmetry axis [as illustrated in Fig. 1(a)]. Further, the symmetry axis of the self-propulsion force is oriented at an angle \(\theta \)  with respect to the laboratory x-axis. The time evolution of \(\theta \)  due to rotational diffusion of the particle is described by Eq. (3). The random forces, \(\lbrace \xi _x(t), \;\xi _y(t), \; \xi _{\theta }(t)\rbrace \)  accounting thermal translational and rotational diffusion have been modelled by Gaussian distributions, zero mean, and \(\delta \) -correlations,
\(\langle \xi _i(t)\xi _j (t^{\prime }) \rangle &=&2 \gamma k_BT \delta _{ij}\delta (t-t^{\prime }); \; i,j=x,y, \\\langle \xi _{\theta }(t)\xi _{\theta } (t^{\prime }) \rangle &=&2D_{\theta }\delta (t-t^{\prime }), \) 
